Method for re-grinding and polishing free-form surfaces, especially rotationally symmetrical aspherical optical lenses

ABSTRACT

A method for re-grinding and polishing free-form surfaces, especially rotationally symmetrical aspherical optical lenses by tools. in which the virtual levelling of a coarsely pre-grinded lens, for example, is calculated by interferometric measurement and by calculation with a desired form; pressure, rotational speed and sojourn time of the tools are controlled by means of said virtual levelling and the surface of the lens, for example, is divided up into partial areas. The partial areas correspond to the size of the tools. A zeroized approximation is calculated for the control of the tools. Said zeroized approximation enables the interaction of the partial areas to be estimated. By taking into account the estimated interaction, a sojourn time for each tool on each partial area is calculated as a function of pressure and rotational speed of the tool for each partial area, using a linear equation system and the tools are controlled accordingly. The invention also relates to tools and tool arrangements in addition to especially precise aspherical lenses.

The invention relates to a method for grinding and polishing offree-form surfaces, in particular of rotationally symmetric asphericaloptical lenses.

In contrast to spherical lenses used in many cases up to now, theseaspherical lenses have special optical properties theoreticallypresenting the physical optimum. In practice, this means that imagesrealized using these aspherical lenses are considerably more luminousintense and focused. They avoid errors such as the spherical aberration.Something similar applies for the even more irregular surfaces which arehere called free-form surfaces. They can assume conical, wavelike,cylindrical or other shapes. The potential fields of application areeven larger for them.

Therefore, the imperative necessity exists to produce these surfacescost-efficiently. This is impossible at present, as all methods in userest on the skills of experienced operators and/or on the use ofproduction automats which do only work with very small tools. Thediameters of these tools are mostly only about a tenth as large as thoseof the workpieces. For this reason, the aspheres produced up to now bygrinding and polishing are very expensive.

The present invention addresses these problem points. On one hand, thegrinding and the polishing and here, particularly, the correspondingcorrection passes are no longer controlled manually, but by a methodaccording to claim 1 and subsequent claims. On the other hand, the toolsdescribed in claim 23 and subsequent claims provide a considerablyhigher, but nonetheless exactly controllable and reproducible removal.The invention enables thus considerably lower production costs.

There have already been several attempts to solve this problem, amongothers by the method of the patent JP9066464. So far, however, withoutsuccess. In the method disclosed in this print, the surface to beprocessed is arranged into areas. Afterwards, all these together arecalculated in a linear system of equations. In practice, it isimpossible to solve such a system of equations in combination witheffective tools for the entire free-form surface. The example describedin aforesaid print does hints at this point by its extreme simplicity.The defect alluded to here is none in the word's sense, because only anearly planar surface is processed. Thus, it is impossible to increasethe accuracy of the surface with this method by accordant control of thetools.

Subject of the invention is to avoid these disadvantages.

This problem is solved by arranging the free-form surface (1 or 4) intoareas (FIG. 1 and FIG. 2), for example according to the tool's size.Each of these areas then still contains a plurality of positionsentering into the calculation and is solved individually with a separatelinear system of equations. As the areas mutually influence each otherresulting from the width of the processing tool, their interaction mustbe taken into account. For this purpose, a zeroth order approximation,which estimates this interaction, enters into the respective linearsystem of equations. This interaction is also shown by the tool (2)positioned on the surface (4) in the area B8, wherein the tool isalthough processing and therefore influencing B7.

Furthermore, all of the workpiece's and tool's specifics such as thespeed of rotation are taken into account. The plurality of solution setsresulting from the plurality of systems of equations are combined againand used for the controlling of the tool during the grinding orpolishing.

Depending on the required accuracy of the surface and the existingerrors in comparison to the diameter of the employed tool, differentsizes of the areas are reasonable. As a result of the areas' interactionamong each other depending on the tools' width, it is reasonable for theareas to have the same width or the double width of the tool (see alsoFIG. 2).

By the control of the influencing factors determining the grinding andthe polishing, there is the possibility to control the removal on thesurface by the dwell time and/or by the speed of rotation and/or by thecontact pressure of the tool and/or by the speed of rotation of theworkpiece.

By use of the method it becomes possible to remove just as much materialfrom the surface that the specified surface emerges such that thelowermost point of the uncorrected (actual) surface (FIG. 5 minima ofthe curve 7), as this one has nearly not been processed, is still partof the generated specified surface. Practically, there has been removedas few material as possible, but nonetheless the specified shape hasbeen realized. The minimal necessary removal has been realized. This isan decisive aspect for reducing the processing time. Up to now, it ismostly polished as long until some time the least accuracy is fulfilled.This leads to the consequence that rather as much material as shown inFIG. 6 curve 13 is removed and thus the processing is extendedneedlessly.

Contrary to arbitrary free-form surfaces, rotationally symmetricfree-form surfaces exhibit a regularity in form of their rotationalsymmetry. It is negligible how the lens is skewed around its symmetryaxis, the cross section of the surface's shape, as for example in FIG. 4surface (1), is invariant. If these surfaces are processed by methodswhich exploit the rotational symmetry (see also FIG. 4), the errors ofthe surface are distributed rotationally symmetric, too. Then it ispossible to carry out the control of the removal only radially. For thecontrol of such a processing, the introduced method is transferred to anone-dimensional form. The virtual removal and the distribution of theareas is limited to the one-dimensional radial area (see FIG. 5). Theprocessing is done under rotation of the tool and the workpiece then.

As no methods exist yet that enable the use of large tools andsimultaneous increase the surface's accuracy or enhance it to aspecified measure respectively, it has always been necessary to reworkmultiply and to remeasure repeatedly.

For the first time, this method enables simultaneously the use of largetools with simultaneous increase of the surface's accuracy in one passof processing. Both aspects in combination with the control of allentities influencing the processing reduce production time to ten orless minutes (compare also the example on the preferred embodiment onthis).

Partly, very high demands are made for the accuracy of surfaces.Nevertheless, the production costs shall be kept low. Up to now, this isimpossible. Even in case of comparatively large and wide errors, smalltools are used, whereby very long production times result. Additionally,the surface is repeatedly measured between the processing passes withuse of both equal and different, exchanged tools. Because of theclamping and unclamping and the necessary measuring time this requires agreat effort which enhances the production costs greatly.

By the tool-specific use of the virtual removal of this method, theresult of a first processing with a larger tool is already known evenwithout remeasurement (see FIG. 7 curve 10). Based on this, a controlfor the subsequent processing with the smaller tool can be calculatedfor a further increase of the accuracy on base of the same methodapplying a different virtual removal specific for this smaller tool. Theoverall processing is considerably shorter than if the last used,smaller tool would have been used from the beginning. The saving of theremeasurement enables further reductions of costs.

To increase the fields of application of the method, overlapping areasare permitted in addition to non-overlapping areas. The areas B1, B2, B3. . . B9 shown in FIG. 10 overlap pairwise to 50%. For example, B3overlaps to a half with B4 and in turn this one overlaps to a half withB5. There exist respectively 16 common mesh points or calculation pointsrespectively.

An extension of the areas' overlap up to the extreme, where adjacentareas differ from each other in one value only, yields so much thebetter controls for the correction of the surface. For the example inFIG. 10, up to 132 areas (B 1, B2, . . . , B 132) would result as aconsequence.

Regarding the areas' overlap, the corresponding statement is also validin the two-dimensional case. The number of areas increases quadraticallyhere as the overlap of the areas is possible in two dimensions.

With this method, it is possible for the first time to produce asphericglass lenses by grinding and polishing within 20 minutes.

In particular, concave lenses pose high demands to the control duringthe processing. Using this method, it is possible for the first time toproduce concave lenses with a best-fit radius of curvature of less than50 mm within 40 minutes by grinding and polishing with a pv-accuracy ofless than 600 nm.

For the decisive reduction of the processing times, this method enablesthe use of tools (2) with diameters of an eighth to a quarter of thediameter of the workpiece (FIG. 11) and is although able to correct thesurface (1) (see also in the example on the preferred embodiment). Incomparison to hitherto tools with a size of about a tenth, a more thansix times larger removal and an corresponding shortening of theprocessing time becomes possible alone by the use of these tools.

Determining for the use of tools are the existing errors (7 in FIG. 12),which must be removed to reach the required accuracy. It is generallyknown that the tools used for the correction may only be as wide as thenarrowest error, here 20 mm, which must be removed. With this method, itis possible to use tools which are twice as wide as the errors to becorrected or have the double diameter of 40 mm respectively. The errorsare corrected as hitherto, however within a fourth of the time, becausethe processing surface is four times as large with the tool being twiceas wide in comparison to the hitherto tool.

To ensure a constant removal over the time, the processing conditionshave to be invariant. Therefore, the polishing or grinding foil (14 fromFIG. 13), which is the material which gets in contact with theprocessing surface shall exhibit a homogenous structure which is freefrom bubbles, cracks or similar things. Additionally, the composition ofthe material itself shall be macroscopically even.

To be although able to ensure an even supply of polishing agent orcooling agent, perpendicular edges 15 (FIG. 13), through which thepolishing agent or cooling agent can take effect approximately evenlybelow the entire surface of the tool, are inserted in this homogenousmaterial of the polishing pad or of the grinding pad.

To further increase the speed of processing, it is necessary to enlargethe area of removal. However, an enlargement of the tools is notpossible, as the necessary accuracy can not be reached anymore then.

This problem is bypassed by using several tools (2) simultaneously onthe free-form surface (1 or 4) for the processing (FIGS. 14 and 15). Thereachable accuracy is just as high as when using only one tool of thissize.

A reproducible removal is achieved here essentially, if the toolsoverlie the surface perpendicularly. FIG. 16 clarifies an arrangement ofseveral tools which are all overlying the surface tangentially.

In the processing of rotationally symmetric free-form surfaces, themovement of each of the tools according to the method described above isadvantageous.

If especially many tools shall process the surface simultaneously, it isadvantageous if the movement of the tools is carried out alongnon-radial lines.

If the tools are particularly arranged then a processing of the surfaceis also then possible and reasonable if the tools do not move.

In this case, it has to be aimed for that in case of a rotatingfree-form surface the tools are arranged in such a way that the entirefree-form surface is processed which is the case in the example fromFIG. 14.

Solely by an arrangement of several tools it is possible to processfree-form surfaces being neither spherical nor planar with more thanfive percent simultaneously processed area of the entire free-formsurface, in a way such that the process remains controllable and keepsits correcting character.

The use of several tools is improved by separately controlling each ofthe single tools.

In case of using many tools, it is simpler, particularly if the handlingsystem of the tools shall be universal for several lenses, if each ofthe tools exhibits a movable foot which ensures the condition that thetool overlies the free-form surface tangentially even in the case of anot fully correct arrangement.

The control of several tools on one free-form surface (1 or 4) istechnologically very demanding, particularly on small surfaces. Ifseveral tools (2) are combined in mechanical compounds, a control of theremoval is still possible with reduced fine mechanical complexity in astill sufficient amount.

The single tools may be combined mechanically in a rod-shaped compound(18) as can be seen in FIG. 18.

Besides, round compounds (17) are a possibility to combine single tools(2). They are advantageous in the sense of tangential overlying thetools especially on a round rotationally symmetric free-form surface(1).

Said compounds are controlled as single tools with a method according toclaim 1 and subsequent claims by taking into account the differentremoval. The virtual removal must be adapted correpsondingly.

EXAMPLE OF AN EMBODIMENT

The example concerns an aspherical optical lens which shall be polishedcorrectively. For this purpose, the lens is measuredinterferometrically. The error distribution measured before theprocessing is shown by FIG. 3. As the preceding polishing has alreadytaken place in a rotationally symmetric manner as can be seen very wellin FIG. 3, the errors existing on the surface are distributedrotationally symmetric. While both the lens and the tool rotate, thetool moves on a radial path while being aligned perpendicularly to thesurface, from the edge of the lens to the lens's center (FIG. 4). Thecorrection of the errors shall be controlled along this way by means ofthe dwell time.

The total error consideration for the correction of this lens, incontrast to general free-form surfaces, is limited to the radial line.For the purpose of a simplified demonstration, a somewhat clear exampleis chosen here. The application of the method to general free-formsurfaces means merely a transformation to two dimensions, thus the usageof an area instead of a (radial) line only.

The error of the entire measured surface is first averaged to the radialintersection. The result is shown by FIG. 5 in curve 7. The inside lying0, the beginning of the axis of abscissae, denotes the lens's center,the end lying on the right denotes the lens's edge. Only the error ofthe surface with a peak to valley (pv) of about 1700 nm is depicted. Inthis example the whole method works with 130 mesh points, on which acalculation is carried out. For each point, the virtual removal isknown. Based on this, one respective dwell time is created and used tocontrol the removal during the processing. Each of these mesh points wascreated with measurement values from FIG. 3. These 130 mesh pointscorrespond to a distance of 20 mm in this example.

The virtual removal of the tool is calculated for the entire surface onbase of a foot print.

Now, the radial working line of 20 mm is divided into areas (FIG. 5).The tool possesses a width of 33 points, about 5 mm. The areas shallhave the width of the tool. Thus, four areas B 1, B2, B3, B4 result. Foreach of these areas, a system of equations is now build and solved,which contains the error of the surface in this area being lowered aboutthe influence on the adjacent areas estimated by means of the zerothapproximation and the virtual removal at each of the 33 points belongingto the area.

As a result, the dwell times 11 depicted in FIG. 8 emerge. The dwelltimes at the respective 33 points, resulting from the four singlesystems of equations, have been put together here. These dwell timescondition the forecasted removal which constitutes from the sum of thecurves 8 and 9 from FIG. 7. The resulting forecasted error distributionof the surface is shown by curve 10.

The processing of the surface with this control of dwell times took 5,48minutes. The radially averaged distribution of the surface after thecorrection is shown by FIG. 9 in curve 12.

Between the mesh points 0 and 70 an accuracy better than 150 nm wasachieved. From the point 70 to the edge of the lens, a pv-accuracy of pv400 nm could be achieved. Thus, the forecasted error distributioncorresponds to the error distribution actually arisen after theprocessing apart from small deviations in the absolute value.

The example shows that the method is able to correct difficult errors ofa surface in extremely short time in the case of using large tools. Anessential part of the shortening of the production time has, in additionto the large tool (diameter ratio tool:workpiece/1:8), the ability ofthe method to remove exactly as much such that only the actuallyexisting error is removed. With the methods uses hitherto, mostly muchmore removal was realized such that the processing took much more time.FIG. 6 shows a curve 13 which illustrates how much too much removal isremoved in such cases. In this case, the processing time would increaseto 20 minutes. Decisive is also that this result was reached in only onepass of processing without repeated remeasuring and reworking.

DESCRIPTION OF THE FIGURES

FIG. 1: Arrangement of a round free-form surface (1) into areas (3) incase of application of the tool (2) with diameter 16 mm (top view ontothe free-form surface)

FIG. 2: Arrangement of a rectangular free-form surface (4) into areas(3) which are delimited by area boundaries (5) which correspond to thesize of the tool (2) (top view into the free-form surface)

FIG. 3: Two-dimensional error distribution (6) of a rotationallysymmetric optical lens (asphere)

FIG. 4: Motion-sequences in case of the processing of a rotationallysymmetric optical lens (1) with a (polishing) tool (2) (sideview/sectional view)

FIG. 5: Radial intersection of the error distribution (7) on therotationally symmetric optical lens from FIG. 4; this corresponds to theminimally necessary removal

FIG. 6: Shifted radial intersection of the error distribution (13) onthe rotationally symmetric optical lens from FIG. 4; this corresponds tothe removal often realized hitherto

FIG. 7: Illustration of the method with actual state of the surface'serror (7), the forecasted removal (sum from 8 and 9) and the forecastedremaining error after the processing

FIG. 8: The dwell times (11) determined by the method

FIG. 9: The remaining error (12) on the surface processed with thesedwell times (11)

FIG. 10: Exemplary distribution of areas (B1, . . . , B9) overlapping to50% within a radial intersection of a rotationally symmetric surface

FIG. 11: Proportions between tool and workpiece 1:8 and 1:4

FIG. 12: Comparison of size between the narrowest error of the errordistribution ( ) and the tool (2)

FIG. 13: Tool with adapted polishing or grinding foil (14) withperpendicular edges (15)

FIG. 14: Arrangement of several tools (2) on the round free-form surface(1)

FIG. 15: Arrangement of several tools (2) on the rectangular free-formsurface (4)

FIG. 16: Arrangement of several tools (2) which overlie the free-formsurface (1) tangentially, i.e. with perpendicular orientation

FIG. 17: Arrangement of round mechanical compounds (18) of tools (2) ona round free-form surface (1)

FIG. 18: Arrangement of rod-shaped mechanical compounds (18) of tools(2) on a rectangular free-form surface (4)

NUMBERS IN THE FIGURES:

-   1=Round free-form surface-   2=Tool-   3=Serially numbered areas (B1, B2, . . . )-   4=Rectangular free-form surface-   5=Area boundaries-   6=Two-dimensional rotationally symmetric error distribution-   7=Radial intersection of the two-dimensional rotationally symmetric    error distribution-   8/9=Forecasted removal-   10=Forecasted remaining error-   11=Determined dwell times-   12=Actually remaining error on the surface-   13=Too large error often removed hitherto-   14=Polishing or grinding foil consisting of homogenous material-   15=Perpendicular edges for supply of polishing agent or cooling    agent-   16=Polishing or cooling agent-   17=Mechanical compound of tools of round type-   18=Mechanical compound of tools of rod-shaped type

1-37. (canceled)
 38. A method for grinding and polishing free-formsurfaces using at least one tool, the method comprising: calculating avirtual removal of a preprocessed optical surface having an initialshape sufficient to achieve a desired shape; dividing the opticalsurface into a plurality of subareas; calculating a zeroth orderapproximation for estimating a mutual interaction for each adjacentsubarea of the plurality of subareas; calculating a dwell time of the atleast one tool for each of the plurality of subareas using a linearsystem of equations, the calculating taking into account the respectivemutual interaction and at least one of a contact pressure, a speed ofrotation, and a behavior of a polishing agent of the at least one tool;and controlling each of the at least one tool for each subarea so as toremove material from the optical surface in accordance with the virtualremoval, wherein the controlling of the tool is performed by controllingat least one of the contact pressure, the speed of rotation, the dwelltime, and a movement of the at least one tool.
 39. The method as recitedin claim 38, wherein the preprocessed optical surface includes arotationally symmetric aspherical optical surface.
 40. The method asrecited in claim 39, wherein the rotationally symmetric asphericaloptical surface includes at least one of a lens and a mirror.
 41. Themethod as recited in claim 38, wherein the preprocessed optical surfaceis pre-grinded.
 42. The method as recited in claim 38, wherein thecalculating of the virtual removal is performed using interferometricalmeasurement and comparison of the initial shape to the desired shape.43. The method as recited in claim 38, wherein a size of each of theplurality of subareas corresponds to a size of the at least one tool.44. The method as recited in claim 38, wherein a size of each of theplurality of subareas corresponds to double a size of the at least onetool.
 45. The method as recited in claim 38, wherein the controlling ofthe at least one tool is performed by varying the dwell time.
 46. Themethod as recited in claim 38, wherein the controlling of the at leastone tool is performed by varying the speed of rotation.
 47. The methodas recited in claim 38, wherein the controlling of the at least one toolis performed by varying a speed of rotation of the optical surface. 48.The method as recited in claim 38, wherein the controlling of the atleast one tool is performed by varying the contact pressure.
 49. Themethod as recited in claim 38, wherein the controlling of the tool isperformed so as to remove only the minimally necessary material for acorrection of the surface.
 50. The method as recited in claim 39,wherein the virtual removal is transferred to an one-dimensional form,and lens is rotating during the grinding and polishing.
 51. The methodas recited in claim 38, wherein the controlling of the at least one toolis performed only once and a total processing time of less than aboutten minutes.
 52. The method as recited in claim 38, further comprisingcontrolling each of the at least one second tool after the controllingof each of the at least one tool, wherein each of the at least onesecond tool is smaller than each of the at least one tool.
 53. Themethod as recited in claim 38, wherein the plurality of subareas do notoverlap with one another.
 54. The method as recited in claim 38, whereinthe plurality of subareas overlap with one another.
 55. The method asrecited in claim 54, wherein the plurality of subareas overlapsubstantially.
 56. The method as recited in claim 38, wherein theplurality of subareas exhibit different sizes.
 57. An aspherical glasslens having an accuracy better than 600 nanometers, grinded and polishedwithin about 20 minutes according to the method recited in claim
 38. 58.An aspherical glass lens having an accuracy better than 600 nanometersand a concave surface, grinded and polished using a BestFit radius ofcurvature of less than 50 mm within a time of about 40 minutes accordingto the method recited in claim
 38. 59. A correction tool for theprocessing of rotationally symmetric free-form surfaces according to themethod recited in claim 38, wherein the correction tool is rotatable andradially moveable, and wherein a ratio of the size of the tool and thediameter of free-form surface is between one eighth and one quarter. 60.A tool for the processing of rotationally symmetric free-form surfacesaccording to the method as recited in claim 38, wherein the tool isrotatable and radially moveable, and wherein a size of the tool is twiceas wide as the narrowest mountain of errors on the free-form surface tobe removed.
 61. The correction tool as recited in claim 59, furthercomprising a polishing or grinding foil including a homogeneousmaterial.
 62. The correction tool as recited in claim 61, wherein thehomogeneous material is free of bubbles and indentations.
 63. Thecorrection tool as recited in claim 61, wherein the tool includes aplurality of indentations from a working surface of the tool havingsteep edges with respect to the working surface, the indentations forsupplying at least one of a polishing agent and a cooling agent.
 64. Anarrangement comprising a plurality of the tools as recited in claim 19for simultaneously processing a first surface of the free-form surface.65. The arrangement as recited in claim 64, wherein each of theplurality of tools is disposed perpendicularly with respect to theoptical surface.
 66. The arrangement as recited in claim 64, whereineach of the plurality of tools moves on a radial line of a rotationallysymmetric free-form surface.
 67. The arrangement as recited in claim 64,wherein each of the plurality of tools moves on a non-radial line of thefree-form surface.
 68. The arrangement as recited in claim 64, whereineach of the plurality of tools does not move on the free-form surface.69. The arrangement as recited in claim 64, wherein each of theplurality of tools are arranged on the free-form surface in such a waythat, in case of a rotating free-form surface, the entire free-formsurface is processed.
 70. The arrangement as recited in claim 64,wherein the first surface amounts is more than five percent of thefree-form surface.
 71. The arrangement as recited in claim 64, whereinthe plurality of tools are controlled separately.
 72. The correctiontool as recited in claim 59 further comprising a movable foot at aprocessing side of the tool, wherein the foot orients itself such thatthe tool overlies the free-form surface tangentially.
 73. Thearrangement as recited in claim 64, wherein the plurality of tools areavailable in compounds.
 74. The arrangement as recited in claim 73,wherein the compounds are rod-shaped.
 75. The arrangement as recited inclaim 73, wherein the compounds are round.
 76. The arrangement asrecited in claim 73, wherein the compounds are positioned across thefree-form surface and moved as a single tool.
 77. The method as recitedin claim 38, further comprising a subsequent polishing of the free-formsurface, wherein the polishing preserves or improves an accuracy of thefree-form surface.